Chapter 865: Chapter 861 Levy Flight Chapter 865: Chapter 861 Levy Flight In front of the narrow cave entrance, Bi Fang identified the animal tracks coming and going.

Some of these footprints had been there for quite some time.

During the dry season, the surface of the African Savanna was hard and rarely retained footprints unless they were from a large reptile like the Komodo Dragon, whose sharp claws, under the weight of its massive body, would leave a line of small holes in the ground.

Most of what the group saw at the entrance were left during the wet season.

Inside the cave, however, there were fresher footprints, claw marks, and hoof prints.

“No large predators.”

After observing for a while, Bi Fang confirmed this.

He then checked the surrounding environment, confirmed that this underground river had only one entrance, and then concealed himself with Harley behind a pile of rocks, preparing to wait for their prey.

Leaning against a rock, Bi Fang sat on the ground, sharpening his spear.

“The quality of life for humans has significantly improved over the past few decades–skyscrapers, bustling streets, beautiful nightscapes, these are no longer novelties.”

“The rapid development of technology has elevated our tastes in life, and things once considered luxuries are now easily attainable.”

“In terms of meals, we no longer just seek to satisfy hunger; we demand a higher quality of taste, we pursue ‘gourmet food.'”
“However, for the wild animals that also inhabit the Earth, filling their stomachs is still their primary concern.”

“Herbivores or omnivores are somewhat better off, with a relatively abundant food source, as long as they aren’t born in deserts or barren lands, there is always something they can eat.”

“The demands are higher for carnivores, which must hunt to obtain their food.”

“During hunting, predators need to match wits and strength with their prey, a test of both energy and physical strength, and even successful hunts do not guarantee long-term food storage, with the risk of being stolen.”

[Cheetah: Raises both hands in agreement]
[Cheetah: That’s right]
[Why tag Cheetah (Dog’s head)]
[If there is discrimination, speak up, let’s all laugh together, haha]
[Harley: What B-netizens]
After sharpening his spear, Bi Fang carried it on his back and then looked for some strongly scented plants nearby to help camouflage his presence.

Perhaps due to being close to a water source, the plants growing in the rock crevices were green, much more vibrant than the bright yellow dry grass seen earlier on the savanna.

“One of our main missions on this trip to the African Savanna is to teach Harley how to hunt, so he won’t be clueless and meatless when he has to live alone on the savanna.”

“But different types of predators have different temperaments, tastes, and physical conditions, which naturally lead to different hunting styles; we have to demonstrate based on the animal’s characteristics.”

“For example, the hunting styles of lions, tigers, and wolves highlight the differences between felids and canids.”

“Lions and tigers have robust builds and are agile, the latter being more solitary; gray wolves are weaker and slower compared to lions and tigers, but their group living significantly enhances their hunting efficiency.”

“Canadian grey wolves, when hunting bison in the snow-covered wild, continuously employ encirclement and harassment tactics to throw the bison herd into chaos and attack individuals that get separated.”

“Cases like Gray Wolf’s, trying to sweep a sheep village single-handedly, are very rare.”

[This is a good example]
[Old Fang is always good with examples]
“Compared to wolves, as a felid, the tiger seems much more aloof, even among lions, which are popularly seen as group hunters, many males and a few females prefer to act alone.”

“Felids focus on ambush in hunting, emphasizing quick, fierce, and accurate. Even though the cheetah is the king of speed, outright chasing, which is costly, isn’t preferred; ambushing is the best choice.”

“That’s why our demonstration will focus on ambushing.”

“However, no matter the strategy, a prerequisite for any hunting action is first being able to find the prey; otherwise, even the most capable hunting skills are merely theoretical.”

“For wild animals, the most natural foraging strategies are actually just following Brownian motion and Levy flight.”

Brownian motion?

Levy flight?

As Bi Fang explained how to find prey, the sudden mention of a physics concept left many viewers puzzled.

[What the heck is Brownian motion?]
[Isn’t Brownian motion random? This doesn’t seem to fit with Master Fang’s usual tracking approach.]
[So, can anyone tell me what Levy flight is?]
[I’m not well-read, hurry up and tell me]
“That’s correct, but finding tracks and figuring out directions is usually done by me–a human.”

“For animals, mastering these concepts is really too demanding on their brains.”

“Most of the animals at the top of the food chain, such as lions, tigers, wolves, eagles, crocodiles, etc., primarily rely on vision to locate their prey.”

“Visual signals do not have a gradient difference; if you can’t see it, you can’t see it; no animal has X-ray vision.”

“Raptors like eagles have a broad visual field and don’t need to exert much effort in feeding, but terrestrial animals like lions and tigers must consider their foraging strategies.”

“Without knowing the exact location of the prey, Brownian motion is the most natural method.”

But before Bi Fang could finish explaining, the audience became even more confused.

[I’m not sure about lions or tigers, but don’t wolves rely on smell? How did it switch to vision?]
[My understanding is being greatly challenged]
[Is the water in the underground river poisonous, and has Master Fang become confused?]
[Are you deceiving me?]
Suddenly, the screen was filled with doubts and questions.

“Ah, actually, people know too little about the world of smells.”

Bi Fang scratched his head, as his audience lacked his keen sense of smell.

The gap in perception made it seem like they were worlds apart.

After much thought, he came up with an example he felt was appropriate.

“Let’s put it this way, if there’s an alarm clock in a room on the second floor of a villa, and you’re sitting in the living room on the first floor, relying solely on your hearing, would you be able to accurately tell which room on the second floor the alarm is in?”

“I think most people wouldn’t be able to, in the world of animals with a keen sense of smell, their sense of smell functions the same way our hearing is functioning right now, knowing the prey is on the second floor but not knowing in which room, plus the sense of smell is more ambiguous than hearing.”

“As long as you stay in one spot for a long time, you can create two potent sources of scent, which you can’t do in the world of sound.”

[A bit confused, but feels like I caught onto something (facepalm)]
[Seems somewhat reasonable]
[Not clear but impressive]
“Everyone is probably familiar with Brownian motion, the perpetual irregular motion of particles suspended in a liquid or gas, a continuous random process.”

“In fact, Brownian motion might not seem like much, but its discovery was a major development in physics, which had a tremendous impact on human understanding of the universe.”

“Many creatures in nature unintentionally abide by this, animals executing Brownian motion, like coming to the second floor, randomly enter a room to search, and from a data perspective, this is still the most efficient method.”

“Its step length follows a normal distribution, just like random motion, both its step length and direction are discrete. Although Brownian motion and random motion are two different concepts, they each developed a different set of theories, but their mathematical essence is the same, regardless of which hunting strategy the predator uses, there’s essentially no difference in efficiency in finding prey.”

“But if predators really moved aimlessly like headless flies performing Brownian motion, could they really find prey effectively?”

Bi Fang raised this question to the audience.

And without needing an answer, he knew that the response was negative.

“In mathematical terms, Brownian motion is just like the free diffusion of molecules, with molecules at unit speed having an average displacement of only the square root of t over time t.”

“If predators used this strategy to find prey, they might have to travel thousands of miles for success.”

“So there’s another mathematical concept before deciding whether the animal is on the first or second floor, which is Levy flight.”

“The discovery of Levy flight was made by French mathematician Benoit Mandelbrot’s mentor, Paul Pierre Levy, who first identified many random motions in life as Levy flights, including a small portion of Brownian motion.”

“This is a more complex concept, I won’t explain much, but everyone is familiar with one example, the flight path of flies, which actually applies Levy flight, making their motion unpredictable and helping flies evade predators and humans trying to swat their tiny heads.”

“Levy flight is a fractal, meaning no matter how much you magnify it, the pattern looks similar to the original.”

“More importantly, Levy flight is a form of random walk, meaning its path cannot be accurately predicted, just like the elusive steps of a fly.”

“Brownian motion has a characteristic, which is that each step’s length is concentrated in one area, plotted on a graph it forms a bell-shaped curve.”

“Levy flight is not like that, in a Levy flight graph, each step’s distance follows a power law.”

“That means, most of the steps during the motion are short, but a few are very long.”

[I’m not good at math, so if you say so, you’re probably right]
[It’s like listening to a heavenly script again]
“Damn, can’t one survive in the wilderness without knowledge of physics and math?”

Most of the audience in the livestream had already been bewildered by this point.

“The different properties of step lengths in Levy flight and Brownian motion directly lead to Levy flight being more efficient than Brownian motion.”

“In the case of taking the same number of steps or covering the same distance, displacement in Levy flight is much greater than in Brownian motion, allowing exploration of a larger space.”

“This is crucial for organisms that need to forage in unknown territories.”

“For example, marine predators such as sharks employ Brownian motion when they know there is food nearby, as Brownian motion helps ‘clean up the plate’–finding and clearing hidden food in a small area.”

“However, when food is scarce and new territories need to be explored, marine predators abandon Brownian motion and instead adopt a Levy flight strategy.”

“If only you had explained it earlier, it’s all about trying your luck.”

“Summary: It’s all about taking chances.”

“I would rank Master Fang’s room alongside Schrodinger’s cat!”

“Black Buckwheat Tea gifted to the host – a yacht*1–though I don’t understand, big props to Master Fang for his professionalism.”

Behind a rock, Bi Fang and a resting Harley scanned their surroundings, wanting to know if any prey was approaching.

They continued chatting with the audience.

“In 2008, a research team from Central Country and Ugly Country published a study on Nature: they equipped 55 different marine predators from the Atlantic and Pacific oceans, including silk sharks, swordfish, blue marlin, yellowfin tuna, sea turtles, and penguins, with trackers and observed their movement patterns over 5700 days.”

“After analyzing 12 million movements, they found that most marine predators showed a preference for Levy-like movement when food was scarce.”

“Interestingly, the distribution of prey like krill also followed the characteristics of Levy flights.”

“Not only that, soil amoebas, plankton, termites, bumble bees, large land herbivores, birds, primates, and indigenous people also showed similar patterns in their foraging routes.”

“Levy flight seems to be a common rule for organisms to survive in environments with scarce resources.”

“For animals wandering the Earth, finding their next meal relies not just on luck but also on advanced mathematics.”

“With almost no knowledge about the distribution of prey, the efficiency of Levy flights far surpasses that of Brownian motion, which could be why they shift to Levy flight mode when trying their luck.”

“Therefore, biologists later proposed the Levy flight foraging hypothesis to summarize the animals’ flamboyant movements when left to fate.”

“However, just because wildlife relies on fate doesn’t mean Harley has to follow suit. We can help it realize that some places are more likely to encounter prey, and simply performing Brownian motion in a few fixed locations can aid its survival on the savanna.”

“Referee, I’m calling a foul for cheating on the other side!”

“Your complaint is invalid!”

“Damn awesome, you’re the first host I’ve seen who seriously discusses mathematical knowledge outdoors.”

“Knowing your math and science well, you wouldn’t fear walking anywhere in the world.”

“You think math and science can’t help you survive in the wilderness, but in reality, you simply don’t know enough and haven’t learned it thoroughly (joking).”

After sitting behind the rock with Harley for half the day, finally, around noon, Bi Fang encountered his first real prey on the savanna.

An ostrich!